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Quillen Grassmannians as non-modular homotopy fixed points

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Abstract.

The aim of this paper is to compute the homotopy fixed points of the homotopy action described by unstable Adams operations on the classifying spaces of unitary groups. The same technique can be applied to compute homotopy fixed points of the action of certain automorphisms on p-compact groups called generalized Grassmannians. We use the description of Quillen Grassmannians to describe the set of homotopy representations of elementary abelian p-groups into them.

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Acknowledgments.

The author is greatly indebted to Carlos Broto for several helpful comments concerning Section 3 and wishes to express her thanks to Jesper Møller for pointing out the existence of he above mentioned exercise in [4] and helpful suggestions to improve results in Section 4. We also thank the referees for their careful reading and many suggestions.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Natàlia Castellana

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  1. Natàlia Castellana
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Correspondence to Natàlia Castellana.

Additional information

Mathematics Subject Classification (2000): 55R35, 55R40, 20D20

in final form: 31 October 2003

The author is supported by CIRIT grant 1995FI-02105PG and partially supported by MCYT grant BFM 2001-2035.

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Castellana, N. Quillen Grassmannians as non-modular homotopy fixed points. Math. Z. 248, 477–493 (2004). https://doi.org/10.1007/s00209-004-0665-9

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